Question

Find the distance between (−8, −3) and (−2, −5) . Round your answer to the nearest hundredth, if necessary.

Answer 1

To find the distance between the points \((-8, -3)\) and \((-2, -5)\), you can use the distance formula, which is given by:

\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]

Here, \((x_1, y_1) = (-8, -3)\) and \((x_2, y_2) = (-2, -5)\).

Plugging in the coordinates:

\[
d = \sqrt{((-2) - (-8))^2 + ((-5) - (-3))^2}
\]

Calculating the differences:

\[
x_2 - x_1 = -2 + 8 = 6
\]
\[
y_2 - y_1 = -5 + 3 = -2
\]

Now squaring those differences:

\[
d = \sqrt{(6)^2 + (-2)^2} = \sqrt{36 + 4} = \sqrt{40}
\]

Now we simplify \(\sqrt{40}\):

\[
\sqrt{40} = \sqrt{4 \times 10} = 2\sqrt{10}
\]

Next, we can calculate the numeric value of \(2\sqrt{10}\):

\[
\sqrt{10} \approx 3.1623 \quad \text{(approx)}
\]
\[
2\sqrt{10} \approx 2 \times 3.1623 \approx 6.3246
\]

Now rounding to the nearest hundredth:

\[
d \approx 6.32
\]

Thus, the distance between the points \((-8, -3)\) and \((-2, -5)\) is approximately \(\boxed{6.32}\).